Classification of Thurston-relation subfactor planar algebras

2016/06/02 by Corey Jones, Zhengwei Liu, Jones, Corey +3
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Geometric and Algebraic Topology #math.OA #math.QA

paper · pdf · doi:10.48550/arxiv.1606.00779

21 pages

arxiv created 2016/06/09 · arxiv updated 2016/06/10

Abstract

Bisch and Jones suggested the skein theoretic classification of planar algebras and investigated the ones generated by 2-boxes with the second author. In this paper, we consider 3-box generators and classify subfactor planar algebras generated by a non-trivial 3-box satisfying a relation proposed by Thurston. The subfactor planar algebras in the classification are either E⁶ or the ones from representations of quantum SU(N). We introduce a new method to determine positivity of planar algebras and new techniques to reduce the complexity of computations.

Related

• Singly generated planar algebras of small dimension, Part III
• Yang-Baxter relation planar algebras
• A planar algebra construction of the Haagerup subfactor
• A generating problem for subfactors
• Universal skein theory for finite depth subfactor planar algebras